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Chapter 0: Problem 5

Evaluate the expressions. $$ \left(\frac{-2}{3}\right)^{2} $$

Short Answer

Expert verified
The value of the expression \(\left(\frac{-2}{3}\right)^2\) is \(\frac{4}{9}\).

Step by step solution

01

Identify the exponent and the base

The expression we want to evaluate is \(\left(\frac{-2}{3}\right)^2\). In this expression, the base is \(\frac{-2}{3}\) and the exponent is 2.
02

Apply rules for even exponents and negative numbers

When a negative number is raised to an even power, the result will be positive. This is because a negative number multiplied by itself results in a positive number, and this applies to our base: \((鈭�2)^2 = (鈭�2)(鈭�2) = 4\)
03

Raise the fraction to the power of 2

Now, we need to raise both the numerator and the denominator to the power of 2: \[\left(\frac{-2}{3}\right)^2 = \left(\frac{(-2)^2}{3^2}\right)\]
04

Simplify the expression

We already know that \((-2)^2 = 4\) from step 2. Now, let's square the denominator: \(3^2 = 3 \times 3 = 9\) Now, substitute these values into the fraction: \[\left(\frac{-2}{3}\right)^2 = \frac{4}{9}\]
05

Final answer

The value of the expression \(\left(\frac{-2}{3}\right)^2\) is \(\frac{4}{9}\).

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Most popular questions from this chapter

Giving the answer as \(a\) whole number or a fraction in lowest terms. $$ 20 /(3 * 4)-1 $$

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